Graph Editor - Active curve name?
As generally we select the object we want to edit, and then operate, this seems a non-well implemented function.
This is the fastest way I've found:
Box select all the objects in the graph editor list, press numpad + three times (until every channel is expanded, press - to collapse).
Select the point you want to edit and press shift H to hide everything else (Alt H to unhide).
The corresponding channel will be the only one with the eye icon active.